Algebra 1 Rational Inequalities

In this lesson we are going to take care of rational inequalities. There are a few different techniques that you could use for solving rational inequalities, but we are going to focus on looking at a table and keeping track of the sign for these. You'll learn the steps to solving rational inequalities, starting by setting the inequality with zero on one side. The next thing is to solve the related equation that is set equal to zero. When solving the related equation, it’s best to combine all rational expressions into one rational expression. This will often involve adding or subtracting rational expressions.

Rational Inequalities

Using the values from step 2 and 3 (critical values) we divide the x-axis into intervals

Use a test point from inside each of the intervals to see if it satisfies the inequality

Check the end points of each interval to see if it satisfies the inequality (Note we never include any values that make the denominator equal to zero)

When solving the related equation, its best to combine all rational expressions into one rational expression. This will often involve adding or subtracting rational expressions.

To better find the critical values, factoring the numerator and denominator of the rational expression will be useful.

Rational Inequalities

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.